Although the info E=200GPa is mentioned in part b, you will need this in part a.
Δd1 and Δd2 represent a stretch in the outer cylinder and a compression of the inner one. In terms of those, what will the tension and compression be (per unit length)? What must the relationship be between the two forces?

Although the info E=200GPa is mentioned in part b, you will need this in part a.
Δd1 and Δd2 represent a stretch in the outer cylinder and a compression of the inner one. In terms of those, what will the tension and compression be (per unit length)? What must the relationship be between the two forces?

Perhaps I misunderstand the arrangement. Any diagram?
I read it that two cylinders have been fabricated, one with an external diameter of slightly over 100mm, the other with an internal diameter slightly under. The larger will not slide over the smaller because of a 4.305x10^-3mm overlap. Through heating, the larger cylinder expands and is slid on, then allowed to cool. This will produce tension in the outer cylinder, increasing its internal diameter to 100mm, and compression in the inner cylinder, contracting its external diameter to 100mm.

Perhaps I misunderstand the arrangement. Any diagram?
I read it that two cylinders have been fabricated, one with an external diameter of slightly over 100mm, the other with an internal diameter slightly under. The larger will not slide over the smaller because of a 4.305x10^-3mm overlap. Through heating, the larger cylinder expands and is slid on, then allowed to cool. This will produce tension in the outer cylinder, increasing its internal diameter to 100mm, and compression in the inner cylinder, contracting its external diameter to 100mm.

Do you read it differently?

Unfortunately no diagraM.
I imagine something like this:

I could be (most likely) wrong so I really don't know.
All I do know is that the thickness of the outer cylinder must equal 2mm, I just don't know how to get there.

Edit: in my textbook/study guide there is no formula for radial stress given "because it is very small and thus disregarded". I am only given formulas for circumferential (hoop) stress and longitudinal stress.

It would help me to follow your working if you would avoid plugging in numbers. Just keep everything algebraic. It's a very good style to adopt, having many advantages.
ri = original outer radius of inner cylinder
ro= original inner radius of outer cylinder
ri-ro=δ (=4.305x10^-3mm)
R= 100mm
To= circumferential tension in outer cylinder, etc.
wo = thickness of outer cylinder, etc.
P= pressure between cylinders = 200kPa.

Using those variables, what is the change in radius of the outer cylinder?
What is the change in circumferential length of the outer cylinder?
What equation does that give for To?
What is the relationship between To and P?
Same as above for inner cylinder.

It would help me to follow your working if you would avoid plugging in numbers. Just keep everything algebraic. It's a very good style to adopt, having many advantages.
ri = original outer radius of inner cylinder
ro= original inner radius of outer cylinder
ri-ro=δ (=4.305x10^-3mm)
R= 100mm
To= circumferential tension in outer cylinder, etc.
wo = thickness of outer cylinder, etc.
P= pressure between cylinders = 200kPa.

Using those variables, what is the change in radius of the outer cylinder?
What is the change in circumferential length of the outer cylinder?
What equation does that give for To?
What is the relationship between To and P?
Same as above for inner cylinder.

Sorry about that I am honestly just grasping at straws.

I have tried to figure out where you want me to go with the above but I just cannot get it.
R=radius? It should then be 100mm/2=50mm?

Is there a specific equation that I am supposed to be using to find the solution?

I have tried to figure out where you want me to go with the above but I just cannot get it.
R=radius? It should then be 100mm/2=50mm?

Is there a specific equation that I am supposed to be using to find the solution?

Yes, sorry, I'm not used to diameters being given instead of radii.

Forcing the cylinders to other than their relaxed radii results in a change in their circumferential lengths. That causes a compression in the one and a tension in the other. These forces must balance.

Forcing the cylinders to other than their relaxed radii results in a change in their circumferential lengths. That causes a compression in the one and a tension in the other. These forces must balance.

Please try to answer my questions in turn. Where do you get stuck?

No problem.
Okay so the inner cylinder is under compression and the outer cylinder is under tension if I imagine the situation.
So tension = compression but I don't know how to put this into an equation with the other variables.

It would help me to follow your working if you would avoid plugging in numbers. Just keep everything algebraic. It's a very good style to adopt, having many advantages.
ri = original outer radius of inner cylinder
ro= original inner radius of outer cylinder
ri-ro=δ (=4.305x10^-3mm)
R= 100mm
To= circumferential tension in outer cylinder, etc.
wo = thickness of outer cylinder, etc.
P= pressure between cylinders = 200kPa.

Using those variables, what is the change in radius of the outer cylinder? ro=ri- 4.305x10^-3mm
What is the change in circumferential length of the outer cylinder? Lo=Li+4.305x10^-3mm
What equation does that give for To? To=P+Ti
What is the relationship between To and P? The pressure between the cylinders increases the tension in the outer cylinder because the inner cylinder is pushing outwards onto it
Same as above for inner cylinder.

Using those variables, what is the change in radius of the inner cylinder? ri=4.305x10^-3mm +ro
What is the change in circumferential length of the inner cylinder? Li=Lo-4.305x10^-3mm
What equation does that give for Ti? Ti=P-To
What is the relationship between Ti and P? The pressure between the cylinders increases the compression in the inner cylinder because the outer cylinder is pushing inwards onto it

As I asked, please do not plug in numbers yet, just use algebraic symbols. Much easier for me to follow what you do.
Anyway, that does not give the change in radius of the inner cylinder. Its outer radius starts at ri. What is its final outer radius?